%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM500+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 12:28:19 PM UTC 2025
% Result : Theorem 35.23s 4.81s
% Output : CNFRefutation 35.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 39 unt; 0 def)
% Number of atoms : 156 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 154 ( 67 ~; 60 |; 19 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(85,plain,
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(sK6(xk))
| ~ doDivides0(sK6(xk),xk)
| ~ isPrime0(sK6(xk)) ),
inference(instantiation,[status(thm)],[85]) ).
fof(mPrimDiv,plain,
! [W0] :
( ( aNaturalNumber0(W0)
& W0 != sz00
& W0 != sz10 )
=> ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
cnf(66,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK6(X0),X0) ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l1,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| doDivides0(sK6(xk),xk) ),
inference(instantiation,[status(thm)],[66]) ).
cnf(67,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(sK6(X0)) ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l62,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| isPrime0(sK6(xk)) ),
inference(instantiation,[status(thm)],[67]) ).
fof(m__2327,plain,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
cnf(83,plain,
xk != sz00,
inference(cnf,[status(esa)],[m__2327]) ).
cnf(l3,plain,
xk != sz00,
inference(instantiation,[status(thm)],[83]) ).
fof(mDefQuot,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00
& doDivides0(W0,W1) )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
cnf(50,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(X2)
| X0 = sz00 ),
inference(cnf,[status(esa)],[mDefQuot]) ).
cnf(l72,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xk != sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(instantiation,[status(thm)],[50]) ).
fof(m__1860,plain,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
cnf(73,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l217,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(instantiation,[status(thm)],[73]) ).
fof(mSortsB_02,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
cnf(4,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
cnf(l190,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(mDefPrime,plain,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
cnf(58,plain,
( ~ aNaturalNumber0(X0)
| X0 != sz00
| ~ isPrime0(X0) ),
inference(cnf,[status(esa)],[mDefPrime]) ).
cnf(l221,plain,
( ~ aNaturalNumber0(xp)
| xp != sz00
| ~ isPrime0(xp) ),
inference(instantiation,[status(thm)],[58]) ).
fof(m__1837,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
cnf(69,plain,
aNaturalNumber0(xm),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l191,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(65,plain,
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK6(X0))
| X0 = sz00
| X0 = sz10 ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l2,plain,
( ~ aNaturalNumber0(xk)
| aNaturalNumber0(sK6(xk))
| xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[65]) ).
cnf(72,plain,
isPrime0(xp),
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l232,plain,
isPrime0(xp),
inference(instantiation,[status(thm)],[72]) ).
cnf(68,plain,
aNaturalNumber0(xn),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l250,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
fof(m__2315,plain,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
cnf(81,plain,
xk != sz00,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l384,plain,
xk != sz00,
inference(instantiation,[status(thm)],[81]) ).
cnf(84,plain,
xk != sz10,
inference(cnf,[status(esa)],[m__2327]) ).
cnf(l64,plain,
xk != sz10,
inference(instantiation,[status(thm)],[84]) ).
cnf(82,plain,
xk != sz10,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l5,plain,
xk != sz10,
inference(instantiation,[status(thm)],[82]) ).
cnf(70,plain,
aNaturalNumber0(xp),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l357,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l100,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l26,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xk != sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(instantiation,[status(thm)],[50]) ).
cnf(l149,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(instantiation,[status(thm)],[73]) ).
cnf(l118,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l119,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l124,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
fof(m__2306,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
cnf(80,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l156,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(instantiation,[status(thm)],[80]) ).
cnf(l21,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xk != sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(instantiation,[status(thm)],[50]) ).
cnf(l192,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(instantiation,[status(thm)],[80]) ).
cnf(l294,plain,
( ~ aNaturalNumber0(xp)
| xp != sz00
| ~ isPrime0(xp) ),
inference(instantiation,[status(thm)],[58]) ).
cnf(l85,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l235,plain,
( ~ aNaturalNumber0(xp)
| xp != sz00
| ~ isPrime0(xp) ),
inference(instantiation,[status(thm)],[58]) ).
cnf(l297,plain,
isPrime0(xp),
inference(instantiation,[status(thm)],[72]) ).
cnf(l379,plain,
xk != sz10,
inference(instantiation,[status(thm)],[84]) ).
cnf(l267,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l448,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l161,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l237,plain,
isPrime0(xp),
inference(instantiation,[status(thm)],[72]) ).
cnf(l41,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l108,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(instantiation,[status(thm)],[73]) ).
cnf(l146,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l197,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l45,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(instantiation,[status(thm)],[80]) ).
cnf(l65,plain,
xk != sz00,
inference(instantiation,[status(thm)],[83]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l62,l3,l72,l217,l190,l221,l191,l2,l232,l250,l384,l64,l5,l357,l100,l26,l149,l118,l119,l124,l156,l21,l192,l294,l85,l235,l297,l379,l267,l448,l161,l237,l41,l108,l146,l197,l45,l65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM500+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 12:29:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.19/0.50 % launching worker at depth: 11
% 35.23/4.81 % SZS status Theorem for theBenchmark
% 35.23/4.81 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------